Because that for his name's sake they went forth, taking nothing of the Gentiles. For his name's sake they went forth - For the sake of preaching the Gospel of the grace of God, and making known Jesus to the heathen.
Taking nothing of the Gentiles - Receiving no emolument for their labor, but in every respect showing themselves to be truly disinterested. Sometimes, and on some special occasions, this may be necessary; but the laborer is worthy of his hire is the maxim of the author of Christianity. And those congregations of Christians are ever found to prize the Gospel most, and profit most by it, who bear all expenses incident to it, and vice versa.
But some construe εξηλθον, they went out, with απο των εθνων, from the Gentiles, or rather by the Gentiles, and give the passage this sense: They went out, i.e., were driven out by the Gentiles, taking nothing with them, i.e., leaving all their property behind, so that they were in a state of great destitution. A curious reading here, εθνικων, heathenish men, for εθνων, Gentiles, which latter might imply those who were converted from among the Gentiles, while the sense of the other term seems to be restrained to those who were still unconverted, may seem to strengthen the above interpretation; and although the construction seems rather harsh, yet it is not, on the whole, unlikely. The reading above referred to is that of the most ancient and reputable MSS. That to be driven out or expelled is one scriptural meaning of the verb εξερχομαι, see Matthew 8:32 : And when they were come out, οἱ δε εξελθοντεσς, and when they were Driven Out. Matthew 12:43 : When the unclean spirit is gone out, εξελθη, is Driven Out. See Mark 5:13, Mark 7:29 : The devil is gone out of thy daughter, εξεληλυθε, is Expelled. Mark 9:29 : This kind can come forth by nothing εν ουδενι δυναται εξελθειν, can be Driven Out by nothing, but by prayer and fasting. Luke 8:2 : Mary Magdalene; out of whom went, αφ' ἡς δαιμονια ἑπτα εξεληλυθει, out of whom were Cast, seven demons. See also 1 John 2:19; Revelation 3:12; and Schleusner, in voc. εξερχομαι.